I need to be able to have the actual files, not only to view and edit via UI.

Evernote is "note" centered (dah!). It's a notebook. But you can attach all sorts of files to them, including audio files & photos (even when recorded/taken directly through the phone app, very handy!)

Plus, it has this web clipper that makes it super easy to grad stuff on the internet an store them in one of your notebooks, putting in some tags on the way.

On computers, ideally I should be able to edit the notes in Emacs, but
not only on the website in a Web browser. This probably mean there
should be a Emacs mode for the note system.

Okay, now is the BEST PART :) it has an awesome command-line tool that runs on linux, called geeknote.me. So basically you can create/edit any of your notes and send it in the could with any editor (but it works better with vim, like everything else, nat(u)rolly ;)

That's the only tools I have used, so maybe there are other good tools out there, but I can definitely recommend the one.
http://evernote.com/

There are a whole bunch of things that satisfy everything but the emacs part of this (Google docs, dropbox, ect) - I'm using a mac and my solution would be to use google docs and then have quickCursor running so that I could edit section of text I wanted in emacs (I currently have it set up to edit everything in vim There are a whole bunch of things that satisfy everything but the emacs part of this (Google docs, dropbox, ect) - I'm using a mac and my solution would be to use google docs and then have quickCursor running so that I could edit section of text I wanted in emacs (I currently have it set up to edit everything in vim (and, in fact, that's how I'm writing this post now).

On a mac I think QuickCursor is your answer, and I'm sure there are similar apps for other OSs - it's a really useful tool. :wp

I'm user of dropbox and plain text files. One huge advantage is very simple editing in android environment. (And probably iphone - I'm not sure). You can even create files in offline mode. There are VIM on android, but I can't be sure it's very useful.

I have pretty much the same use requirements, and have ended up using Dropbox and Epistle. It's a flexible combination, stores all content in plain ASCII text, and supports Markdown. I use Org-mode and MobileOrg on top of that, and they actually coexist rather nicely after some configuration.